如何计算Exponential Dist
learn.whatIsHeading
Analyzes exponential distribution (waiting time) with mean 1/λ, used for modeling queues and failures.
公式
Mean = 1/λ, Variance = 1/λ²
分步指南
- 1PDF: f(x) = λe^(-λx)
- 2CDF: F(x) = 1 - e^(-λx)
- 3Mean = 1/λ, Variance = 1/λ²
- 4Memoryless property: P(X > s+t | X > s) = P(X > t)
例题解析
输入
λ=0.5, x=2
结果
P=0.368
常见错误注意事项
- ✕Using normal distribution for time data (exponential better)
- ✕Wrong λ parameter (rate, not 1/rate)
- ✕Not checking memoryless property applicability
常见问题
What's practical use?
Customer arrivals (Poisson), equipment failures, radioactive decay, service times.
What's memoryless property?
Past waiting time doesn't affect future; no "aging" effect.
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